A simplified analytical model of sound propagation in the human ear

Abstract

AbstractA simple mechanical model of sound propagation in the human ear from the entrance to the ear canal up to the round window membrane is outlined. The model shows the outer, middle and inner ear as two waveguides connected by a lever mechanism. The case when a sound wave from a sound source at a given frequency and intensity goes into the ear is considered. The sound as a plane elastic wave in the air of the ear canal is partially reflected from the eardrum and after relocation by a lever of the ossicles; it runs as a plane elastic wave in the cochlea fluid to be finally damped at the round window membrane. The basilar membrane excited by the running sound wave in the cochlea is taken as a chain of separate fibers. The power of the sound reaching the ear is compared with the power of the sound carriers in the ear. As a result, simple rules for the amplitude of the stapes footplate as well as for the amplitude and pressure of the forced acoustic wave in the cochlea are obtained. The formulas for the amplitudes of the membrane of the round window and the basilar membrane are also shown. The results of calculations based on these rules were compared with the measurements made on temporal bone specimens. The tests were done for the level of the sound source intensity of 90 dB and a set of frequencies from the range of 400-10,000 Hz. The amplitudes of the stapes-footplate and the round window membrane were measured. A mean difference, between the calculated and the measured values, for the stapes-footplate reached 31%, and for the round window membrane, it was 21%. A ratio of the basilar membrane velocity to the stapes footplate velocity as a function of the frequencies was shown. The obtained graph was close to that got by others as a result of the measurements.